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The generic quantum superintegrable system on the sphere and Racah operators. (arXiv:1608.04590v3 [math-ph] UPDATED)

来源于:arXiv

We consider the generic quantum superintegrable system on the $d$-sphere with
potential $V(y)=\sum_{k=1}^{d+1}\frac{b_k}{y_k^2}$, where $b_k$ are parameters.
Appropriately normalized, the symmetry operators for the Hamiltonian define a
representation of the Kohno-Drinfeld Lie algebra on the space of polynomials
orthogonal with respect to the Dirichlet distribution. The Gaudin subalgebras
generated by Jucys-Murphy elements are diagonalized by families of Jacobi
polynomials in $d$ variables on the simplex. We define a set of generators for
the symmetry algebra and we prove that their action on the Jacobi polynomials
is represented by the multivariable Racah operators introduced in
arXiv:0705.1469. The constructions also yield a new Lie-theoretic
interpretation of the bispectral property for Tratnik's multivariable Racah
polynomials. 查看全文>>